# Index fund example 1 what is the portfolio weight in

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Index Fund Example 1 What is the portfolio weight in the index fund such that the expected return on your portfolio is 20%? 0.20=w(.12)+(1-w)(.02) implies w=1.8 Given that your equity is \$20,000, what is the dollar amount you invest in the index fund? 20000*1.8=36000 Given the price of the fund is \$40 per share, how many shares of the index fund do you buy? 36000/40=900 How much money do you need to borrow? 36000-20000=16000 What is the standard deviation of your portfolio? 1.8(.17)=0.306 What is your 5% Value-at-Risk? .20-1.64*.306= -30.18% 17

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Index Fund Example 2 Make all the assumptions for Index Fund  Example 1  except now You want to buy the fund on margin such that your  portfolio standard deviation is 0.05   18
Index Fund Example 2 What is the portfolio weight in the index fund such that the standard deviation of your portfolio is .05? 0.05=w(.17) implies w=0.29 Given that your equity is \$20,000, what is the dollar amount you invest in the index fund? 20000*.29=5800 Given the price of the fund is \$40 per share, how many shares of the index fund do you buy? 5800/40=145 How much money do you invest in the risk-free asset? 20000-5800=14200 What is the expected return of your portfolio? .29*.12+(1-.29)*.02=4.9% What is your 5% Value-at-Risk? .049-1.64*.05= -3.33% 19

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Improving Client’s Position 20 A client asks your advice about her investments. She has  invested \$70,000 in a Mosaic mutual fund and \$10,000 in risk- free bonds. She asks you whether she should re-allocate her  assets.  Mosaic fund Expected return: 15%  Standard deviation: 30%.  Vanguard Fund  Expected return: 12%  Standard deviation: 16%.  The risk-free rate is currently 7% (borrowing and lending)
Improving Client’s Position  21 Question 1:  What is the expected return and  the standard deviation of her current portfolio?  The expected return is:  E(r)=(7/8)*(0.15) + (1/8)*(0.07) = 14% (stat rule 1) The standard deviation is:  Stdev(r)=(7/8)*0.30 = 0.2625 (stat rule 2)

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Increasing E[r] with same  σ 22 Question 2:  Assume that she can borrow and lend at an  interest rate of 7%.  Can you find a portfolio with same total risk but higher  expected return?
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